Abstract
In this paper, we obtain atomic decompositions for the spaces H1,q, 1 < q < ∞ (this case has not been considered earlier) and show that a multiplier that satisfies the condition of the Marcinkiewicz theorem acts from the space H1 into H1,∞. Bibliography: 5 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland (1986).
R. Fefferman and F. Soria, “The space weak H 1,” Studia Math., 85, 1–16 (1986).
F. J. Ruiz and J. L. Torrea, “Calderón-Zygmund theory for operator-valued kernels,” Advances Math., 62, 1–46 (1986).
A. Torchinsky, Real-variable Methods in Harmonic Analysis, Academic Press (1986).
I. Stein, Singular Integrals and Differential Properties of Functions [Russian translation], Moscow (1973).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 150–167.
Rights and permissions
About this article
Cite this article
Parilov, D.V. Two theorems on the Hardy-Lorentz classes H 1,q . J Math Sci 139, 6447–6456 (2006). https://doi.org/10.1007/s10958-006-0362-9
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10958-006-0362-9